The symplectic extensions obtained by capping boundary components, are as we have seen, often somewhat inefficient in terms of the dimensions they add. We close by recalling two classical constructions which accomplish the same task, essentially by adding a trivialisation to our connections on a base point on each boundary circle. The first, due to Alekeev Malkin and Meinrenken [1]} takes us outside of the symplectic domain, into quasi-Hamiltonian territory; the second involves the extended moduli spaces of Jeffrey [2]}. The reduction to the flat connection spaces are then group quotients. We note that there is an “imploded” version of the construction of [1]}, considered in [4]}.
